Question

1)test reivew:Let F⃗ (x,y,z)=6x2i⃗ −sin(xz)(i⃗ +k⃗ ). Calulate the divergence:
div F⃗ (x,y,z)=

Answer 1

\[\boldsymbol{\vec F}(x,y,z) = 6x^2\boldsymbol{\hat\imath}-\sin(xz)(\boldsymbol{\hat\imath}+\boldsymbol{\hat k})\]

\[\text{div}\boldsymbol{\vec F}(x,y,z) =\nabla\cdot\boldsymbol{\vec F}\\\qquad\qquad\qquad=\frac{\partial F_x}{\partial x}+\frac{\partial F_y}{\partial y}+\frac{\partial F_z}{\partial z}\]

Answer 2

First resolve the function into its components

\[\boldsymbol{\vec F}(x,y,z)=F_x\boldsymbol{\hat\imath}+F_y\boldsymbol{\hat\jmath}+F_z\boldsymbol{\hat k}\]

Answer 3

Then take the respective partial derivatives of the components

and add them together